Delft University of Technology
Uncorrelated Interference in 79 GHz FMCW and PMCW Automotive Radar
Overdevest, Jeroen; Jansen, Feike; Laghezza, Francesco ; Uysal, Faruk; Yarovoy, Alexander DOI
10.23919/IRS.2019.8768181 Publication date
2019
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2019 20th International Radar Symposium (IRS)
Citation (APA)
Overdevest, J., Jansen, F., Laghezza, F., Uysal, F., & Yarovoy, A. (2019). Uncorrelated Interference in 79 GHz FMCW and PMCW Automotive Radar. In P. Knott (Ed.), 2019 20th International Radar Symposium (IRS) (pp. 1-8). [8768181] IEEE . https://doi.org/10.23919/IRS.2019.8768181
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Uncorrelated Interference in 79 GHz FMCW and PMCW
Automotive Radar
Jeroen Overdevest∗, Feike Jansen∗, Francesco Laghezza∗, Faruk Uysal∗∗, Alexander Yarovoy∗∗
∗NXP Semiconductors N.V.
Eindhoven, The Netherlands
email: jeroen.overdevest@nxp.com, feike.jansen@nxp.com, francesco.laghezza@nxp.com
∗∗Delft University of Technology
Delft, The Netherlands
email: f.uysal@tudelft.nl, a.yarovoy@tudelft.nl
Abstract: An extensive comparison on radar-to-radar interference in frequency-modulated continuous wave (FMCW) and binary phase-frequency-modulated continuous wave (PMCW) radars is performed. The noise-plus-interference power for FMCW-to-FMCW and PMCW-to-PMCW interference in a single victim and single interferer environment is compared for generalized waveform-based scenarios. It is proven that the interference suppression is equal in FMCW and PMCW radars in case the time-bandwidth product in both systems is equal.
1
Introduction
Radar sensors have become fundamental instruments in automotive safety applications and ad-vanced driver assistance systems (ADAS). The ADAS applications, such as automatic emer-gency braking (AEB), adaptive cruise control (ACC), and lane keeping assist (LKA), set high requirements on performance robustness for the safety of human life. To enable new applica-tions, which requires wider coverage, the number of radar sensors per car will increase and data from multiple sensors will be fused. In line with this trend, the number of cars utilizing multiple high-end radar sensors is likely to increase as well (so-called radar penetration rate), which leads to an increased probability of radar-to-radar interference resulting in performance degradation. Interference avoidance techniques, mitigation techniques and a possible radar MAC layer [1] will need to be exploited to counteract the challenges.
Interference in FMCW radars has been a well-established research topic which has been math-ematically substantiated by multiple researchers [2, 3, 4, 5]. In contrast, PMCW-to-PMCW interference is a less studied phenomenon. Beise [6] and Bourdoux [7] investigated interfer-ence scenarios in FMCW and PMCW automotive radars, but these were mainly case studies, not substantiating the effects of radar-to-radar interference with respect to receiver sensitivity or dynamic range losses. Also, PMCW radars face more challenges in mitigating the noise-like interference, while for FMCW radars mitigation techniques exist, e.g. using time-domain
The 20th International Radar Symposium IRS 2019, June 26-28, 2019, Ulm, Germany 978-3-7369-9860-5 c 2019 DGON
notching [4], time-domain reconstruction [8], sparse sampling approaches [9], or (hybrid) digi-tal beamforming techniques [10].
This paper studies multi-user interference and provides a detailed, generalized and non-situation specific, waveform-based study. The paper is organized as follows. Section 2 introduces the basic fundamentals and the measures required to analyze radar-to-radar interference. Sec-tions 3 and 4 provide a detailed investigation substantiated with numerical results on uncor-related and quasi-coruncor-related interference, respectively. Finally, conclusions are drawn in Sec-tion 5.
2
FMCW and PMCW Waveform Analysis
In FMCW radar, the transmitters modulate the carrier by linearly increasing the frequency over time for a predefined interval Tp, known as a chirp. The FMCW chirp can be defined by its
quadratic phase, given as φM(t) = πB/Tpt2 with B the radio frequency (RF) chirp bandwidth,
which is incorporated in,
sT X(t)=cos 2πfct + φM(t) + φ0 rect t − mTp/2 Tp (1) where φ0is any arbitrary initial phase and rect denotes the rectangular function. Then, a series of
Np chirps is induced to be able to estimate target velocities. FMCW radars make use of stretch
processing, which possesses the desirable characteristic to convert the wideband reflected chirps into narrowband signals. A time-delayed target reflection results in a (narrowband) difference frequency (the so-called beat frequency) between the local oscillator (LO) and the accordingly received echo, which is proportional to the target’s range. Phase shifts along the slow-time samples can determine the target’s velocity. Using 2D FFT processing, the range and velocity of multiple targets can be efficiently retrieved.
PMCW waveforms are constructed using a code sequence of length Lc. The duration of a single
coded sequence is equal to Tp = LcTcwith Tcthe duration of a chip. A sequence of Npcodes are
transmitted concurrently, having a total measurement time of T = NpTp. Equation 1
incorpo-rates the bits of the selected sequence with phase shifts φM(t) ∈ {0, π} using binary phase-shift
keying (BPSK) modulation. The waveform is modulated on a single-carrier frequency fc. After
the analog down-conversion, the target’s range profile is retrieved by correlating the received signal with the transmitted code, while the target’s velocity is estimated in a similar way as in FMCW radar.
FMCW and PMCW are pulse compression waveforms that entail an increase in range resolution and signal-to-noise ratio (SNR). The SNR gain depends on the time-bandwidth product (BT ) of the modulated waveform [11]. In FMCW radars, the BT -product of a single chirp in real Nyquist sampled receivers can be presented in logarithmic form
BTp = 10 log10(BIFTp) + GLP F = 10 log10 (Fs/2) Tp + GLP F = 10 log10(Ns/2) + GLP F, (2)
where BIF represents the intermediate frequency (IF) bandwidth, Nsthe number of real-valued
ADC samples, and GLP F the gain achieved by low-pass filtering the down-converted signals.
Table 1: System Parameters
(a) FMCW
Parameter Symbol Value
Chirp Bandwidth B 300 MHz Chirp Repetition Interval Tp 10.64 µs
Sampling rate Fs 40 MHz No. of Samples Ns 426 No. of Chirps Np 1024 Measurement Time T 10.9 ms Time-Bandwidth Product BT 65.15 dB (b) PMCW
Parameter Symbol Value Code Length Lc 3868
Bit rate Rb 300 MHz
Code Repetition Interval Tp 12.89 µs
Sampling rate Fs 300 MHz
No. of Samples Ns 3868
No. of Code Repetitions Np 845
Measurement Time T 10.9 ms Time-Bandwidth Product RbT 65.15 dB
Stretch processing transforms (desired) target reflections into narrowband baseband signals, while (undesired) noise and interference signals are spread into wideband signals which can be (partly) suppressed by low-pass filtering. Therefore, this gain can be approximated with GLP F ≈ 10 log10(BRF/BIF)with BIF = Fs/2. By coherently adding a series of Np consecutive
chirps, the SNR can be further increased by a factor Np. Thus, the time-bandwidth product of
the entire burst of chirps equalsBT(dB)= 10 log10(NsNr/2) + GLP F.
Similarly, the BT -product for a single code in PMCW systems equals the code length BTp =
Lc. Again, coherent summation of the slow-time periods results in a gain equal to Np. Therefore,
the time-bandwidth product of the total code is BT = LcNc. Table 1a and 1b present the
configurations of the reference systems used in this paper. The reference systems are designed to have equal time-bandwidth products for the total measurement duration. In both radars, the transmission parameters are as follows: transmit power PT = 10 dBm, the transmit and receive
antenna gain GT = GR= 12 dBi, and carrier frequency fc= 79 GHz. Let’s shortly introduce
(a) Instantaneous frequency in FMCW radars. (b) Time-invariant, sinc-shaped spectrum of single-carrier binary PMCW waveforms. Figure 1: Different time-frequency interference phenomena in FMCW and PMCW radars.
the interference behavior in frequency and time for FMCW and PMCW waveforms. Figure 1a depicts the instantaneous carrier frequency of an FMCW waveform. After the analog mixing stage in the receiver, the difference signal of KT targets and KI FMCW interferers can be
expressed over time as follows, sBB(t) ∝ KT X k=1 exp j2π fc,Sτ + BS Tp,S τkt − BS 2Tp,S τk2 rect t − Tp,S − τk Tp,S + KI X l=1 exp j2π (fc,I,l− fc,S)t + fc,I,lτl+ B I,l 2Tp,I,l − BS 2Tp,S t2− BI,l 2Tp,I,l (2tτl+ τl2) rect t − Tp,I,l− τl Tp,I,l (3) where τ denotes the victim-to-interferer time delay, the parameter subscripts S and I denote the source and interferer, respectively. Equation 3 shows that the interference signal after mixing still is in the form of a frequency ramp due to its quadratic phase.
Figure 1b shows the frequency spectrum of a PMCW waveform. Due to the rectangular-shaped chips used in the coded waveform, the spectrum of an PMCW waveform has a sinc-shape. The spectrum is non-interrupted, time-invariant due to a 100% duty cycle to leverage the more en-hanced periodic correlation properties. This means that the interference energy will be present for consecutive ADC samples in the source, while FMCW-to-FMCW interference has a discon-tinuous interference presence as a result of the low-pass filtered de-ramped signal.
This paper considers uncorrelated interference, meaning that the source and interferer waveform do not share the exact same time-instantaneous resources: carrier frequency fc, bandwidth B,
and code properties (family, code itself, and length). A very specific case with distinctive overlap in time of the victim and interference waveforms, which we will refer to as quasi-correlated interference, results in a different interference behavior that will be addressed in Section 4.
3
Uncorrelated Radar-to-Radar Interference
Radar-to-radar interference might occur when two radars with common field of view trans-mit an arbitrary waveform, illuminating each other by line-of-sight (LOS) or non-line-of-sight (NLOS), and sharing time and frequency resources, which can be defined in ratios as γT = TI/TS and γB = BOL/BS, respectively. Here, two source and interfering signal vectors,
sRX,S(t) and sRX,I(t), share the same bandwidthBOL= (BS+ BI)/2 + |fc,I− fc,S|. Now, a
gener-alized non-waveform based interference scenario can be defined using the triplet (γT, γB, PR,I),
with PR,I being the received interference power at the victim antenna.
For numerical analysis, we have sketched the following scenario: three static targets at distances RT = 5, 30, 60 m all having a radar cross section (RCS) of 0 dBsm, and a single interferer at
RI = 10 m. Figure 2a shows the Range-Doppler map in the absense of interference where all
targets can be detected. The (desired) target reflected signals experience the coherent processing gain according to the RF time-bandwidth product relative to the noise power, thus resulting in a signal-to-noise ratio (SNR) gain. In this case, the noise floor is equal to the thermal noise power, which depends on the receiver bandwidth BIF, and is PN(dB) = −174 + FN = −159 dBm/Hz
given the receiver noise figure FN = 15 dB.
With the victim configuration according to Table 1, results of having an active inter-ferer illuminating the victim are shown in Figure 2b-2f for a received interference power PR,I(dB) = −56.40 dBm at the victim’s receive antenna, where the signal covers the complete
victim’s RF bandwidth γB = 100% and has a time presence of γT = 100%. Figure 2b presents
a FMCW-to-FMCW interference scenario where the interfering chirp is completely random-ized and incoherent in time during the acquisition period Tp,S. Then, the interference energy
spreads out uniformly. However, in practice the frequency chirp and time (PRI) for both the source and interferer do not change during the measurement time TS (as depicted in Figure 1a).
In this scenario, the noise floor is not completely flat, showing specific (diagonal) patterns, due to the residual coherence over the slow-time samples, after Doppler processing. By observing Figure 2d-2f, PMCW interference can be classified as highly uncorrelated leading to an uni-form increase in noise floor. The interference samples appear as noise, therefore, the victim’s correlation output is undeterministic. Hence, no apparent pattern along the slow-time periods is observable after range and Doppler processing. Therefore, the consecutive slow-time outputs of range processing are incoherently added in the Doppler FFT, leading to the noise-like behavior.
(a) (b)
(c) (d)
(e) (f)
Figure 2: Non-interfered scenario in (a) and uncorrelated interference scenarios for (b-c) FMCW-to-FMCW and (d-f) PMCW-to-PMCW with different interference configurations: (d) dif-ferent code families [APAS(3868), ZCZ(4096)], (e) difdif-ferent code length [APAS(3868), APAS(3864)], and (f) different bit rates [APAS(3868), APAS(1308)].
Using the link budget model, the noise-plus-interference power can be theoretically expressed as,
IN = 10 log10(PN + PR,I10m) − 10 log10(BIF) = −141.1 dBm/Hz. (4)
Comparing (4) to the results of uncorrelated interference from Figure 2, shows that the noise floors in the Range-Doppler Maps measured in power spectral den-sities yield in (2b) −143.05 dBm/Hz, (2c) −144.15 dBm/Hz, (2d) −146.91 dBm/Hz, (2e) −145.86 dBm/Hz, and (2f ) −145.93 dBm/Hz. The decrease in dynamic range due to interference presence causes the targets at RT = 30 and 60 m to fall below the noise floor. The
measured values are slightly lower compared to the value calculated in (4). In addition to the average noise floor increase given the interference time occurrence γT as defined in [12], the
in-terference power present after processing also depends on the time interval taking into account the FFT window suppression,
PI,post−proc = PR,I(dBm)− 10 log10(γT) − Lwin, (5)
where Lwindefines the suppression gain from the applied window.
To further explore the interference energy levels in FMCW and PMCW radars, a series of Monte Carlo simulations have been executed considering randomized interference occurrences and configurations. The randomized parameters include fc, B, Tp, as well as the code selected from
its family for PMCW interference. Figure 3 shows the comparison among the simulated noise floors Range-Doppler outputs for the FMCW and PMCW reference systems in the presence of increasing received interference power levels. Respectively, Figures 3a-3c depict the noise floor outputs for the time-occurrences γT = 5%, 25%, and 70%, which can be individually compared
using (5). Small differences in the post-processing noise floor between the FMCW and PMCW reference systems can be explained by disparities in the architectural designs.
(a) (b) (c)
Figure 3: Measured noise floor levels [in dBm/Hz] for different interference occurrences in time: (a) γT = 5%, (b) γT = 25%, and (c) γT = 70%.
4
Quasi-correlated Radar-to-Radar Interference
In contrast to uncorrelated interference, situations can arise where radar-to-radar interference results in a non-uniform increase of the noise floor after post-processing. Regardless of the frequency or coding resources, this occurs when the pulse repetition interval (PRI) of the victim
and interferer is in the form of Tp,S = nTp,I with n being an integer or its reciprocal.
For example, when n = 2, every slow-time period of the victim fits in precisely two periods of the interferer. This means that the phase-relation over the slow-time samples remains constant, and the interference energy is concentrated in a single dimension in the zero-Doppler cut. In case the interferer is moving, or radiating at a deviating carrier frequency, the ridge is moving to the corresponding offset Doppler frequency. As the offset in carrier frequency exceeds the victim’s maximum unambiguous velocity, the ridge aliases to the negative frequencies due to back-folding. This phenomenon of spectrum folding withholds the system from estimating the corresponding frequency offset, because of ambiguity.
The effects of quasi-correlated interference have been presented in Figure 4, for n = 2, for FMCW and PMCW, respectively, in which a distance ridge is concentrated in the zero-Doppler gate, since both victim and interferer are transmitting at similar carrier frequency fc and are
moving at zero relative radial speed. For FMCW-to-FMCW, the RF chirp bandwidth was equal for both cases BS = BI = 300 MHz with the victim’s chirp time Tchirp,S = 12.8 µs and reset
time Treset,S = 10.3 µs, and the interferer’s chirp time Tchirp,I = 8.09 µs and reset time Treset,I =
3.46 µs. Hence, both victim’s and interferer’s period duration Tp = Tchirp+ Tresetsatisfy Tp,S =
2Tp,I. Similarly, the quasi-correlated interference situation for PMCW was configured with both
victim and interferer transmitting at a similar bitrate Rb, but using code lengths of Lc,S= 4096
and Lc,I= 2048, respectively.
(a) FMCW-to-FMCW
(b) PMCW-to-PMCW Figure 4: Quasi-correlated interference with equivalent PRIs: TS = 2TI
5
Conclusion
In this paper, we have investigated and compared the impacts of uncorrelated and quasi-correlated interference on FMCW and PMCW radar systems. Regardless of the waveform being used, the interference energy after range and velocity processing is equal, and it behaves accord-ing to the RF time-bandwidth product. Both radar systems have to account for similar losses in the receiver sensitivity assuming an equal received interference power.
For FMCW, uncorrelated interference leads to a diagonal ridges in the range-Doppler spectrum that depends on the ratio between the slopes of the victim and interferer. In PMCW radars, the interference energy is uniformly spread out over the whole Range-Doppler map.
Also, we have presented under which conditions (equal or multiple PRIs) a form of quasi-correlated interference can arise for both reference systems.
6
Future Work
The conclusion that FMCW and PMCW pulse-compressed waveforms experience equivalent interference-driven noise floors, according to the RF time-bandwidth product, does not indicate that the chance on interference for both radar systems is equal when taking into account wave-form and system architecture aspects. Therefore, before being able to claim which wavewave-form can better reject interference, the probability of interference occurrence in FMCW and PMCW radars needs to be identified, including a study on the probability of uncorrelated and correlated interference.
7
Acknowledgments
This paper has emerged from the first author’s Master Thesis from Delft University of Technol-ogy, which was done in cooperation with NXP Semiconductors. The first author wants to show his gratitude to both organizations for the provided facilities, supervision, and assistance.
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